the notice mentioned by Tom says that, as the codice fiscale takes some
letters from your first name and surname, two people born on the same day
and in the same city can get the same code if their names are similar. This
is the reason the original code is assigned to every individual shortly
after birth by the Ministry of Finance, who keeps record of all the
generated codes.
And a word of caution: using an unofficial (auto-generated) code is
misrepresenting yourself and you can be prosecuted for it.
After all, I wouldn't give to a US officer a phony SS number just because I
don't have one, and you?